The frontier of quantitative finance, in one feed. The newest peer-review-bound research from arXiv’s q-fin archive — trading and market microstructure, portfolio management, risk, pricing, and machine learning in markets — with titles, authors, and abstracts, linked straight to source. Updated continuously.
Stochastic calculus and the theory behind the models.
Ruibo Ma
Assuming that the asset price $X$ follows a constant elasticity of variance process, this paper studies the optimal prediction problem $\inf_{0\leq τ\leq T}\mathbb{E}|X_τ-\ell|$, where the infimum is taken over stopping times $τ$ of $X$ and $\ell$ is a hidden aspiration level independent of $X$. Adopting the aspiration level hypothesis, w…
Kenichiro Shiraya, Tomohisa Yamakami, Akira Yamazaki
This paper proposes a stochastic discount factor (SDF) scaled by time-varying volatility. By utilizing prices and market data implied solely from S\&P 500 options, the proposed framework recovers a stable, non-monotonic SDF that captures the pure forward-looking expectations of market participants while mitigating observation noise. Our e…
Ying Chen, Hoa Nguyen, Julian Sester, Hoang Hai Tran +1
We study sequential decision making under evolving uncertainty in high-frequency financial markets, where changing market dynamics continually challenge static decision policies. We show that robustness has two economically meaningful dimensions: uncertainty tolerance, which determines how much uncertainty the decision maker allows, and a…
Mohammad Abedi
Standard models of stock price dynamics and option valuation usually begin by postulating stochastic processes. This paper develops an entropic inference framework that derives these processes from information constraints. The key symmetry is that markets reward returns rather than price levels, which selects log price as the dynamical va…
Hao Qin, Ruozhong Yang, Charlie Che, Liming Feng
Many quantitative finance methods and applications are formulated in terms of option-implied risk-neutral marginals rather than directly in terms of option prices. Representative examples include martingale optimal transport, Bass local-volatility calibration, scenario analysis, and option-implied tail-risk measurement. The desired risk-n…
Wolfgang Breytmann, Julio Deride, Nicolás Hernández
We study the stability of solutions to the discrete-time contingent-claim problem over a finite investment horizon when uncertainty is modeled by random variables with finite discrete support. Our main contribution is to use Rockafellian perturbations as a framework for this stability analysis: we construct perturbations of the underlying…
Chris Angstmann, Tim Gebbie
We derive an operational-time variance kernel for a latent-order-book reaction boundary and use it to separate three objects usually collapsed in calendar-time volatility models: a structural boundary cumulant, a clock projection, and a pricing-measure choice. The reaction boundary is the zero of a bid--ask imbalance field. For a locally …
Yang Zhou, Jianwen Chen, Ruipeng Wei
Three quantitative predictions have been advanced for the square-root law (SRL) of market impact, $I/σ_D = c\,(Q/V_D)^δ$ with $δ\approx 0.5$: GGPS ($δ=β-1$), FGLW ($δ=α-1$), and LOB walking ($δ=1/(1+γ)$). Using a minimal limit-order-book model populated by heterogeneous interacting agents and calibrated against the Tokyo Stock Exchange be…
Umut Çetin, Mingwei Lin
We study a one period limit order market with informed traders, noise traders, and competitive liquidity suppliers, in which the number of informed traders is random. Liquidity suppliers know the distribution of the informed trader count, but not its realization, and therefore face uncertainty about both the presence and the intensity of …
Aleš Černý, Johannes Ruf, Martin Schweizer
Uniformly weighted divergence preferences (UWDP) introduced in Maccheroni et al. (2006) are an important class of risk-averse preferences that contain as a special case the monotone mean--variance utility. UWDP are characterised by the lowest expected value of an act in $L^\infty$ under an adversarially chosen probability measure combined…
Joseph Leclère, Youssef Ouazzani Chahdi, Mathieu Rosenbaum, Grégoire Szymanski
Market impact is defined as the difference between the observed price trajectory under a given execution strategy and the counterfactual trajectory that would have prevailed without it. Since this counterfactual is unobservable, estimating market impact requires simulating alternative paths under the same realized market randomness. We ad…
Miquel Noguer i Alonso
Financial markets are hard to predict, not because price moves are purely random, but because structure is strategic, capacity-constrained, and computationally difficult. Classical information theory measures uncertainty, dependence, and directed flow through entropy, KL divergence, NMI, and transfer entropy. This paper extends that found…
Useong Shin
I propose a cap-axis integral diagnostic for factor-model evaluation. Low-dimensional factor models can improve the maximum-Sharpe frontier while leaving zero-alpha violations on economically fixed subspaces. The diagnostic studies one such subspace by lifting pricing errors into a bridge-alpha curve along the market-capitalization rank a…
Dannin J. Eccles, Roger Lee
We consider a class of partial-information portfolio optimization problems in which the drift of a risky asset is driven by two latent stochastic factors evolving at distinct time scales. We show that the filtered estimate of the latent mean-reversion level is driven by the difference between fast and slow exponential moving average (EMA)…
Umut Çetin, Mingwei Lin, Giulia Livieri
When is a large trade news, and when is it a liquidity shock? We study this question in a sequential competitive limit order book with asymmetric information. In our model, liquidity suppliers observe aggregate order flow but not its decomposition into informed demand and uninformed liquidity demand. We model uninformed order flow with St…
Miquel Noguer I Alonso, Ali Al Fallouji
Tail-risk management is not only an instrument-selection problem. It is an allocation problem across loss mechanisms: abrupt crash states, volatility repricing, and persistent drawdowns require different forms of protection. This paper develops a continuous-time CVaR framework that places two common protection sleeves -- long out-of-the-m…
Corrado De Vecchi, Max Nendel, Steven Vanduffel
We study risk aggregation problems for arbitrary non-decreasing aggregation functions and tail risk measures under dependence uncertainty in a distributionally robust setting. To this end, we introduce the notion of hidden dependence for random vectors, which is built on the concepts of risk concentration and common tail events developed …
Matteo Ferrari, Roger J. A. Laeven, Emanuela Rosazza Gianin, Marco Zullino
Financial resilience concerns the rate at which a position recovers, or further deteriorates, in response to adverse conditions. As a first step, Laeven, Ferrari, Rosazza Gianin, and Zullino (arXiv:2505.07502) introduced the resilience rate, defined as the expected instantaneous rate of (favorable) change of a price or risk-assessment pro…
Jongjin Park, Hyungbin Park
This paper studies the recovery of uncertainty from dynamic sublinear valuation rules. A robust valuation assigns each payoff its worst-case expected value across plausible models under uncertainty and induces a dynamic sublinear valuation rule. While valuation rules are observable in practice, the underlying uncertainty structure is late…
Chunle Huang
In this paper, based on the concept of weighted distribution, we introduce a kind of new approximations for sums of lognormal random variables, such that they are both comonotonic and moment matching. Numerical results show that the approximation performance of the newly presented approximations is, overall, comparable to the classical co…
Raphael Coelho
The Fundamental Theorem of Asset Pricing states that a market is free of arbitrage exactly when it admits an equivalent martingale measure. We formalize it in Lean 4 over Mathlib in three settings: a finite-state market over a finite horizon (Harrison-Pliska), a one-period market on an arbitrary probability space with a single scalar retu…
Riccardo Alberti, Sven Karbach
We study the variance-optimal hedging of European contingent claims written on forwards. We assume that the dynamics of the underlying forward curves follow a Heath--Jarrow--Morton--Musiela stochastic partial differential equation modulated by an infinite-rank stochastic covariance component. The variance-optimal hedge is then given by th…
Miquel Noguer i Alonso
This paper develops a path-first theory using the signature as a universal coordinate for deterministic paths, rough paths, jump streams, and path-valued random variables. Geometricity is presented as a first-order algebraic property with second-order obstructions: a bracket for non-geometric lifts, and a covariance when averaging random …
Benjamin Avanzi, Bernard Wong, Jinxia Zhu
Modern resolution and prudential regimes increasingly wind up a distressed firm not at a single hard threshold but through a graduated, state-dependent process. We study how the design of such a regime shapes the trade-off between shareholder value and financial stability for a firm whose surplus follows a general diffusion. Forced liquid…
Elham Soufiani, Mehrdad Pirnia
This paper presents a multi-period mixed-integer linear programming (MILP) framework for planning the transition from conventional to electric aircraft in regional aviation. The model jointly optimizes fleet acquisition, infrastructure deployment, and service allocation over time, while accounting for policy constraints such as emissions …
Daniele Angelini
Testing self-similarity in fractional processes from a single observed trajectory is difficult under long-range dependence, because the associated Kolmogorov--Smirnov (KS) statistic undergoes a phase transition when $H>1/2$. In this regime, the classical limit collapses to a non-functional absolute Gaussian law and finite-sample convergen…
Leif Andersen, Andrey Itkin, Rakhymzhan Kazbek
A flexible forward (FF) is a customized FX hedging instrument that guarantees a fixed exchange rate while letting the holder choose the delivery date within a pre-agreed window. It is therefore an American-style option on timing, and its valuation must respect the volatility skew of the underlying currency pair. We price FF contracts (and…
Miquel Noguer I Alonso, Rodolfo Pereira Franklin
Financial return forecasting is a difficult test case for time-series foundation models (TSFMs) due to low signal-to-noise ratios, structural breaks, heavy tails, and weak persistence. This paper benchmarks pretrained TSFMs against train-from-scratch neural baselines in a deliberately conservative financial setting. We evaluate TimeGPT/Ti…
Xingyu Ren, Michael C. Fu, Pierre L'Ecuyer
Leibniz derivative estimation is a Monte Carlo technique for estimating derivatives of a discontinuous sample performance in stochastic models with respect to parameters of interest. By combining the push-out likelihood ratio (LR) method with Leibniz integral rules, it generalizes a broad class of existing LR-based derivative estimators. …
Christian Laudagé
Monetary risk measures quantify the risk of uncertain monetary payoffs (or losses), whereas in time series analysis risk is typically assessed using logarithmic returns. Return risk measures (RRMs) provide an axiomatic foundation for this latter approach, which relies crucially on the positive cone of the space of essentially bounded rand…
Yue Cao, Guohui Guan, Zongxia Liang, Xiaodong Luo
This paper studies a singular dividend control problem for a firm with heterogeneous shareholders whose discount rates follow a given distribution. The central planner aggregates expected discounted payoffs using an ambiguity aggregation function $phi$, which captures shareholder heterogeneity and ambiguity attitudes but also leads to tim…
Andy Au
A Bayesian investor learns an unknown asset drift by Kalman-Bucy filtering and trades the mean-variance optimal portfolio, but his observation model may be wrong. We make the policy robust to an adversary who distorts the law of observed prices, paying for it in relative entropy. Because wealth and beliefs are driven by the same Brownian …
Jian Sun
For a fixed maturity, an arbitrage-free option smile induces natural normalized strike coordinates. This paper makes three contributions. First, it gives an elementary discrete no-arbitrage proof of monotonicity for the central Black--Scholes normalized coordinate \(k/v(k)\), using only finite-strike comparisons, convexity, monotonicity, …
Sandhya Devi
In this work, we develop a method to estimate the relaxation time (the time required to reach equilibrium) of a nonextensive system such as financial market dynamics, using a Euclidean Gradient Flow (EGF) framework for the maximization of Tsallis entropy. The equilibrium state is defined as the maximum-entropy state. Specifically, the dyn…
Madhurendra Mishra, Armaan Aryan, Arsh Gogia, Adarsh Ganesan
Frequency combs are discrete, equally spaced, phase-coherent spectral lines that emerge from nonlinear mode coupling in physical systems. We show that the incommensurate fractional-order financial model of Huang, Li, Ma, and Chen, whose Caputo derivatives encode macroeconomic long-range memory, generates an analogous structure in its stea…
Boris Günther, Thomas Kruse, Ludger Overbeck, Thorsten Schmidt
We extend the classical theory of affine processes to a path-dependent setting by introducing path-dependent coefficients and provide analytic formulas for their Fourier--Laplace transform in terms of generalized Riccati-type equations. In the proposed framework, we define path-dependent affine processes through their exponential-affine F…
Debora Daniela Escobar, Wing Fung Chong
This paper studies centralized risk sharing with endogenous prices. Multiple policyholders transfer risks to a central insurer through indemnity decisions, while prices are determined by pricing functionals applied to ceded risks. The resulting problem is multiobjective, with Pareto optimality as the natural efficiency criterion. We show …
Shantanu Awasthi, Minglian Lin, Blair Faber, Michael Roberts +1
The Black-Scholes model has been extensively used for option pricing, but exhibits limitations in its reliance on geometric Brownian motion and fixed volatility assumptions. This paper proposes an enhanced model incorporating stochastic volatility with jumps modeled by a Lévy process. Leveraging multidimensional Itô calculus, we derive a …
Jagdish Gnawali, Abootaleb Shirvani, Dilmi C. W. Hettiachchi-Halpe-Kankanamalage, W. Brent Lindquist +2
Classical option pricing models, such as Bachelier and Black--Scholes--Merton, postulate symmetric Brownian diffusion, which limits their capacity to reflect empirical phenomena including return skewness, heavy tails, and volatility asymmetry. This paper develops an innovative extension: the Geometric Asymmetric Brownian Motion (GABM), un…
Farbod Ghasemlu
We study the fee policy of a liquidity provider (LP) in a constant-product automated market maker (AMM) whose fee can be adjusted continuously, as enabled by programmable hooks. Building on the loss-versus-rebalancing (LVR) framework of Milionis et al. (2022) and its extension to nonzero fees by Milionis et al. (2024), we model the LP's w…
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